Optical system and eye piece

ABSTRACT

An eye piece (EL 1 ) is formed having a first lens (L 1 ) having a positive refractive power and a second lens (L 2 ) having a positive refractive power, which are disposed in order from an object (O), and a contact multi-layer diffractive optical element (DOE), which has a first optical element ( 51 ) formed with a relief pattern and a second optical element ( 52 ) which is in contact with the surface of the first optical element ( 51 ) where the relief pattern is formed, is disposed on an optical surface of the first lens (L 1 ) or the second lens (L 2 ).

TECHNICAL FIELD

The present invention relates to an optical system using diffraction,and more particularly to an optical system used for compact, light andhigh performance observation optical systems and projection opticalsystems.

TECHNICAL BACKGROUND

Optical elements using refraction (mainly made of glass) have frequentlybeen used for general optical systems, in order to improve opticalperformance, particularly image formation performance with decreasingamount of aberrations. However aberration correction flexibility must beimproved in order to sufficiently decrease Seidel's five aberrations andchromatic aberration on reference spectral lines, and because of this,the number, size and weight of the optical elements often increase.

To prevent this, an eye piece (optical system) where a plano convexshaped first lens and a plano convex shaped second lens are disposed, ina state of respective convex surfaces facing each other, and adiffractive grating surface is formed on one of the optical surfaces ofthe first lens and second lens has been proposed (e.g. see JapanesePatent Application Laid-Open No. H11-38330). Thereby an eye piece inwhich lateral chromatic aberration is well corrected can be obtainedwith a simple configuration of a small number of lenses, while insuringa predetermined eye relief.

DISCLOSURE OF THE INVENTION Problems to be Solved by the Invention

In the case of the above mentioned eye piece, however, the opticalcharacteristics (lateral chromatic aberration) with a central wavelength(e.g. d-line) are good, but the optical characteristics in otherwavelength areas are not so good.

With the foregoing in view, it is an object of the present invention toprovide an optical system with which good optical characteristics can beimplemented in all areas of the wavelengths to be used, and an eye piecehaving this optical system.

Means to Solve the Problems

To achieve this object, an optical system according to the presentinvention is comprised of a first lens and a second lens having apositive refractive power which are disposed in order from an object,characterized in that a contact multi-layer diffractive optics which hasa first optical element formed with a relief pattern and a secondoptical element which is in contact with the surface of the firstoptical element where the relief pattern is formed, is disposed on anoptical surface of the first lens or the second lens.

In the above invention, it is preferable that the difference ofrefractive index on the d-line between the first optical element and thesecond optical element is 0.45 or less, and the condition of thefollowing expression is satisfied: “0.002<D/f<2.0” where D is an airdistance on an optical axis between the first lens and the second lens,and a focal length of the entire optical system is f.

In the above invention, it is preferable that the condition of thefollowing expression is satisfied: “0<D/ (f1×f2)<0.15” where f1 is afocal length of the first lens, f2 is a focal length of the second lens,and f1>0 and f2>0.

In the above invention, it is preferable that the condition of thefollowing expression is satisfied: “−0.1<D/(f1×f2)<0” where f1 is afocal length of the first lens, f2 is a focal length of the second lens,and f1<0, f2>0, and |f1|>|f2|.

In the above invention, it is preferable that at least one opticalsurface of the first lens and the second lens is aspherical.

In the above invention, it is preferable that the contact multi-layerdiffractive optics is formed on a surface of the first lens, the surfacefacing the object.

In the above invention, it is preferable that the first optical elementis formed using one of a material with a relatively high refractiveindex and low dispersion, and a material with a relatively lowrefractive index and high dispersion, and the second optical element isformed using the other one of the materials, and the condition of thefollowing expression is satisfied: “50<Δνd/Δnd<2000” where Δνd is adifference of Abbe numbers between the first optical element and thesecond optical element, and Δnd is a difference of refractive indexes ona d-line between the first optical element and the second opticalelement.

In the above invention, it is preferable that the condition of thefollowing expression is satisfied: “(Eg+EC)/2>0.9×Ed” where Ed is adiffraction efficiency of the contact multi-layer diffractive optics ona d-line, Eg is a diffraction efficiency of the contact multi-layerdiffractive optics on a g-line, and EC is a diffraction efficiency ofthe contact multi-layer diffractive optics on a C-line.

In the above invention, it is preferable that the condition of thefollowing expression is satisfied: “0.0001<p/f<0.003” where p is aminimum pitch of the relief pattern, and f is a focal length of theentire optical system.

In the above invention, it is preferable that the condition of thefollowing expression is satisfied:

0.1<φ·R/f ²<2.0

where f is a focal length of the entire optical system, φ is a pupildiameter, and R is eye relief.

An eye piece according to the present invention is an eye piece forobserving an image of an object, having the optical system according tothe present invention.

ADVANTAGEOUS EFFECTS OF THE INVENTION

According to the present invention, good optical characteristics can beimplemented in all ranges of the wavelengths to be used.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 are cross-sectional views of multi-layer diffractive optics,where (a) is a cross-sectional view of a non-contact multi-layerdiffractive optics, and (b) is a cross-sectional view of a contactmulti-layer diffractive optics;

FIG. 2 is a diagram depicting a configuration of an optical systemaccording to Example 1;

FIG. 3 are graphs showing various aberrations of the optical systemaccording to Example 1;

FIG. 4 is a graph showing a diffraction efficiency of the contactmulti-layer diffractive optics with respect to each wavelength;

FIG. 5 is a diagram depicting a configuration of an optical systemaccording to Example 2;

FIG. 6 are graphs showing various aberrations of the optical systemaccording to Example 2;

FIG. 7 is a diagram depicting a configuration of an optical systemaccording to Example 3; and

FIG. 8 are graphs showing various aberrations of the optical systemaccording to Example 3.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Embodiments of the present invention will now be described withreference to the drawings. Attempts have been made to include adiffractive optical surface in an optical system, so as to implementhigh performance and compactness which a dioptric system or catoptricsystem cannot implement. However in such a single layer diffractiveoptics having a diffractive optical surface, a flare is generated by thelights in a wavelength area which deviated from a designed wavelength,and this flare could damage image quality and image formationperformance, therefore the use of this diffractive optics is limited toa single wavelength, such as a laser light source or narrow wavelengtharea.

Recently, a diffractive optics called a “multi-layer type” (or laminatedtype) is being proposed. This type of diffractive optics has adiffractive optical surface which is formed saw tooth (relief pattern),and is a plurality of diffractive elements having a different refractiveindex and dispersion value layered with or without contact, andmaintains a high diffraction efficiency roughly in an entire area of adesired wide wavelength area (e.g. visible light range), that is, thewavelength characteristic is good. For details on the characteristics ofsuch diffractive optics, see “An Introduction to Diffractive OpticalElement”, supervised by The Society of Applied Physics (Optical Societyof Japan), Revised Edition, 2006. The data on the diffractive opticalsurface shown in the examples is indicated by an ultra high refractiveindex method, details of which are also included in “An Introduction toDiffractive Optical Element”, supervised by The Society of AppliedPhysics (Optical Society of Japan), Revised edition, 2006.

Concerning structure, the multi-layer diffractive optical element iscomprised of a first optical element 51 made from a first material and asecond optical element 52 made from a second material of whichrefractive index and dispersion value are different from those of thefirst optical element 51, as shown in FIG. 1( a), and the surfaces ofthe optical elements 51 and 52 which face each other are formed to besaw tooth. Then the height h1 of the relief pattern of the first opticalelement 51 is determined to be a predetermined value, and then height h2of the relief pattern of the second optical element 52 is determined tobe a different predetermined value, so as to satisfy the achromaticcondition for a predetermined two wavelengths. Thereby the diffractionefficiency for the predetermined two wavelengths becomes 1.0, and thequite high diffraction efficiency can also be implemented for otherwavelengths. The diffraction efficiency means ratio of intensity I₀ ofthe light which enters the diffractive optics and intensity I₁ of theprimary diffracted light, that is η(=I₁/I₀) in a transmission typediffractive optics.

In the case of non-contact multi-layer diffractive optics DOE′ shown inFIG. 1( a), the first optical element 51 and the second optical element52 constituting the diffractive optics DOE′ have relief patterns 53 and54 of which heights h1 and h2 are different from each other, so aplurality of dies are required, and the first and second opticalelements 51 and 52 must be individually manufactured using these dies,and must be accurately aligned, therefore production takes an enormousamount of time.

To prevent this, a contact multi-layer diffractive optics DOE, where theheight h1 of the relief pattern 53 of the first optical element 51 andthe height h2 of the relief pattern 54 of the second optical element 52are matched, is being proposed (see FIG. 1( b)). This contactdiffractive optics DOE has a configuration in which the second opticalelement 52 is bonded on the surface of the first optical element 51where the relief pattern 53 is formed, and compared with the non-contacttype, manufacturing is easier, such as the error sensitivity (tolerance)of the height of the diffraction grating is less strict, and the errorsensitivity (tolerance) of the surface roughness on the grating surfaceis less strict, therefore the contact type diffractive optics excels inproductivity and mass producibility. This means that the contact typediffractive optics has an advantage in decreasing cost of opticalproducts. By using a contact multi-layer type configuration for thediffractive optics, the diffractive optics can be used for roughly theentirety of wavelengths, and can easily be used for a camera lens of acamera which utilizes white light in a wide band, or for an eye piecewhich is used in a visible light range.

The present invention relates to a compact and light weight opticalsystem using this contact multi-layer diffractive optics. The opticalsystem of the present embodiment is comprised of a first lens and asecond lens having a positive refractive power which are disposed inorder from an object, and a contact multi-layer diffractive optics isformed on an optical surface of the first lens or the second lens.Thereby a compact and high performance optical system, which has goodoptical characteristics in the entire area of wavelengths in use, can beimplemented. This optical system can also be used as a camera lensoptical system, and can also be used as a projection optical system byinstalling a display element near the image surface.

It is preferable to dispose the contact multi-layer diffractive opticson the surface of the first lens facing the object side. Then the lightfrom the object enters the relief pattern of the contact multi-layerdiffractive optics roughly vertically. Therefore the generation of straylight, due to oblique rays which did not enter at a normal angle at thestep difference portion of the relief pattern, can be decreased. Alsothe diffractive optics positioned closest to the object is the contacttype, so the stray light, other than lights which transmit through therelief pattern reflected by the lens surface and lens barrel, andaffecting the image plane, can be decreased.

If the entire diffractive optics has a positive refractive power, it ispreferable that the first optical element has a positive refractivepower, but the second optical element may have a positive or negativerefractive power. These optical elements can be constructed according tothe design requirements, so that specification implementation andaberration correction becomes easier. If the diffractive optical surfacehas a positive refractive power, negative dispersion is generated, sogood achromatism can be implemented in the entire diffractive optics.

The optical elements constituting the contact multi-layer diffractiveoptics must be made from a material having a relatively high refractiveindex and low dispersion, and a material having a relatively lowrefractive index and high dispersion, and it does not matter whichoptical element is closer to the object. Specifically it is necessarythat the first optical element 51 (see FIG. 1( b)) is formed using oneof the material having the high refractive index and low dispersion, andthe material having the low refractive index and high dispersion, andthe second optical element 52 (see FIG. 1( b)) is formed using the othermaterial, and this is an essential configuration requirement to form thecontact multi-layer diffractive optics. In order to decrease errorsensitivity in manufacturing, the difference of refractive indexes on ad-line between the first optical element 51 and the second opticalelement 52 is preferably 0.45 or less, and is more preferably 0.2 orless.

According to the present embodiment, the condition given by thefollowing conditional expression (1) is satisfied,

0.002<D/f<2.0   (1)

where D is an air distance on the optical axis between the first lensand the second lens, and f is a focal length of the entire opticalsystem.

The conditional expression (1) specifies an appropriate range of the airdistance D between the first lens and the second lens by a ratio withthe focal length f. If this conditional expression (1) is satisfied, anoptical system having good optical characteristics can be implementedeven if the overall length is short. If D/f exceeds the upper limit ofthe conditional expression (1), the overall length of the optical systembecomes too long, which makes it difficult to implement compactness andincreases the generation of axial aberrations, so good image formationperformance cannot be implemented. In particular, coma aberration of therays above the principal ray increases and distortion to the + sidetends to generate easily.

If D/f is less than the lower limit of the conditional expression (1),the eye pupil position of the optical system becomes too close, andtends to deviate from the condition to enter near the telecentric areaof an image sensing element, for example. In this case, shading iseasily generated as the image height is higher. Also correction of comaaberration tends to be insufficient, and sufficient image formingperformance cannot be implemented. In the conditional expression (1), itis preferable that the upper limit of D/f is 1.0, and the lower limitthereof is 0.003.

In the conditional expression (1), it is more preferable that the upperlimit of D/f is 0.1, and the lower limit thereof is 0.003.

In this case, it is also preferable that at least one optical surface ofthe first lens and the second lens is aspherical. By this, variousaberrations, such as axial aberration, can be well corrected even if thecontact multi-layer diffractive optics is used, and the overall lengthof the optical system is decreased.

The focal length f of the entire optical system is calculated by thefollowing expression (21), as a composite focal length of the thin lenssystems using the following expression (21), where f1 is the focallength of the first lens and f2 is a focal length of the second lens.The expression (21) can be transformed to be the expression (22).

1/f=(1/f1)+(1/f2)−D/(f1×f2)   (21)

D/(f1×f2)={(1/f1)+(1/f2)}−1/f   (22)

Based on expression (22), if f1>0 and f2>0, it is preferable to satisfythe condition given by the following conditional expression (2).

0<D/(f1×f2)<0.15   (2)

The conditional expression (2) shows that sufficient refractive powerfor the entire optical system can be obtained by decreasing the distanceof the first lens and the second lens with respect to the predeterminedvalues of f1 and f2, if the value of D/(f1×f2) is small enough to beroughly zero. Thereby an optical system (e.g. eye piece) having largerefractive power, of which overall length is decreased by decreasing thedistance between the lenses, can be implemented.

If D/(f1×f2) exceeds the upper limit of the conditional expression (2),the refractive power of the entire optical system weakens, andsufficient refractive power (magnification) cannot be obtained. Also thedistance between the lens and the image plane becomes too short, and itbecomes difficult to arrange the mirror and prism. Also the distortionto the − side increases too much, and good images cannot be obtained. Ifthe lenses contact, the interference fringe enters near the optical axisand the lens surfaces are scratched, so the lower limit of D/(f1×f2)should be 0. In the conditional expression (2), it is preferable thatthe upper limit of D/(f1×f2) is 0.1.

If f1<0 and f2>0, and |f1|>|f2|, it is preferable to satisfy thecondition given by the following conditional expression (3).

−0.1<D/(f1×f2)<0   (3)

If the first lens has a negative refractive power and the second lenshas a positive refractive power, an achromatic function is generated bythe lenses, so the pitch of the relief pattern to implement apredetermined achromatism can be lower. This decreases the generation offlares and makes it easier to manufacture diffractive optics, butdecreasing the distance of the lenses decreases the refractive power.The conditional expression (3) shows an appropriate balance of theoverall length, refractive power and aberrations of the optical system.

If D/(f1×f2) exceeds the lower limit of the conditional expression (3),the distance between the lenses increases, which increases the overalllength and makes it impossible to implement a compact optical system.The distortion to the + side also increases too much, and good imagescannot be obtained. If the lenses contact, the interference fringeenters near the optical axis and lens surfaces are scratched, so theupper limit of D/(f1×f2) should be 0. In the conditional expression (3),it is even more preferable that the upper limit of D/(f1×f2) is −0.01.

It is preferable to satisfy the condition given by the followingconditional expression (4),

50<Δνd/Δnd<2000   (4)

where Δνd is a difference of the Abbe numbers between the first opticalelement 51 and the second optical element 52, and Δnd is a difference ofthe refractive indexes on the d-line between the first optical element51 and the second optical element 52.

The conditional expression (4) specifies an appropriate range of thedifference Δνd of the Abbe numbers and the difference Δnd of therefractive indexes between the material having a high refractive indexand low dispersion and the material having a low refractive index andhigh dispersion. If the range specified by the conditional expression(4) is deviated from, the height of the relief pattern increases or thediffraction efficiency, with respect to various wavelengths, drops, evenif the contact multi-layer diffractive optics is made from a materialhaving a high refractive index and low dispersion and a material havinglow refractive index and high dispersion. In the conditional expression(4), it is preferable that the upper limit of Δνd/Δnd is 800, and thelower limit thereof is 100.

It is preferable to satisfy the condition given by the followingconditional expression (5),

(Eg+EC)/2>0.9×Ed   (5)

where Ed is a diffraction efficiency of the contact multi-layerdiffractive optics on the d-line, Eg is a diffraction efficiency of thecontact multi-layer diffractive optics on the g-line, and EC is adiffraction efficiency of the contact multi-layer diffractive optics onthe C-line.

The conditional expression (5) specifies an appropriate range of thediffraction efficiency in the wavelengths of a broadband. If the rangespecified by the conditional expression (5) is deviated from, thediffraction efficiency in either short wavelengths or long wavelengthsdrops, which increases diffraction flares and diminishes image quality.Specifically, a diffraction flare of blue increases if Eg drops, and adiffraction flare of red increases if EC drops, and both diminish theimage quality. In the conditional expression (5), it is preferable thatthe coefficient related to Ed is set to the 0.8 to 0.98 range, where thevalue 0.9 is a value based on the experience of many individuals using asample extraction.

If the contact multi-layer diffractive optics, which is disposed on anoptical surface of the first lens or the second lens, is symmetric withrespect to the optical axis, and has a diffractive optical surface(relief pattern) where the incident angle of the outermost ray(principal ray) is 10 degrees or less, it is preferable to satisfy thecondition given by the following conditional expression (6)

0.1<C/f<3.0   (6)

where C is an effective diameter of the diffractive optical surface, andf is a focal distance of the entire optical system.

The conditional expression (6) specifies an appropriate range of aneffective diameter of the diffractive optical surface. If C/f exceedsthe upper limit of the conditional expression (6), the effectivediameter becomes too large, which makes manufacturing of the diffractiveoptical surface (relief pattern) difficult, and increases cost. Alsodestructive light easily enters the diffractive optical surface from theoutside, which tends to cause a drop in image quality due to flares. IfC/f exceeds the lower limit of the conditional expression (6), on theother hand, the effective diameter of the lens on which the diffractiveoptical surface is formed becomes small, and the pitch of the reliefpattern decreases, which not only makes manufacturing of the diffractiveoptical surface (relief pattern) difficult and increases the cost, butalso generates flares on the diffractive optical surface and drops imagequality. In the conditional expression (6), it is even more preferablethat the upper limit of C/f is 0.8, and the lower limit thereof is 0.1

If the surface of the first lens facing the object is a concave surface,the surface of the first lens facing the opposite of the object side isa convex surface, and the contact multi-layer diffractive optics isformed on one of these surfaces, it is preferable to satisfy thefollowing conditional expression (7),

0.05<h/d<2.0   (7)

where h is the height of the relief pattern, and d is a smaller one ofthe thickness of the first optical element on the optical axis and thethickness of the second optical element on the optical axis.

The conditional expression (7) shows a relationship between anappropriate height h and thickness d of the optical element when arelief pattern, of which groove height is low, is formed. If h/d exceedsthe upper limit of the conditional expression (7), the height of thegroove becomes relatively too high, which not only makes it difficult toform the relief pattern, but also increases the step difference of thegroove, and easily generates stray light due to the scattering of thelight contacting this step difference portion. If h/d is lower than thelower limit of the conditional expression (7), on the other hand, theoptical elements becomes relatively too thick, which not only makes itdifficult to form the relief pattern, but also increases the internalabsorption of the light in the optical elements, and drops the imagequality due to the drop in transmittance of the entire optical systemand achromatism. In the conditional expression (7), the upper limit ofh/d may be 1.0, and the lower limit thereof 0.02.

It is also preferable to satisfy the condition given by the followingconditional expression (8),

0.0001<p/f<0.003   (8)

where p is a minimum pitch of the relief pattern, and f is a focallength of the entire optical system.

The conditional expression (8) specifies an appropriate ratio of theminimum pitch p and the focal length f of the entire optical system. Ifthe minimum pitch p is small, the angle of diffraction becomes large,and the color dispersion of the diffractive optical surface increases,which is effective for correcting chromatic aberration, but makesprocessing difficult and increases the generation of flares on thediffractive optical surface. Therefore it is important to set theminimum pitch p in an appropriate range.

If p/f iexceeds the upper limit of the conditional expression (8), theminimum pitch p becomes too large, and sufficient achromatism cannot beimplemented, and image quality drops. If p/f exceeds the lower limit ofthe conditional expression (8), the minimum pitch p becomes too small,and as mentioned above, processing becomes difficult, and flares on thediffractive optical surface are generated more frequently. Unnecessaryflare light drops the image quality and drops the diffraction efficiencyas well.

When an image formed using a compact display or an objective lens isenlarged and observed, as an application of the optical system of thepresent embodiment, it is preferable to satisfy the condition given bythe following conditional expression (9),

0.1<φ×R/f ²<2.0   (9)

where f is a focal length of the entire optical system, φ is a pupildiameter, and R is an eye relief.

The conditional expression (9) shows an appropriate relationship of thepupil diameter φ, eye relief R and focal length f when the opticalsystem of the present embodiment is applied to the above mentionedobservation optical system. Securing sufficient eye relief R is criticalto construct an observation optical system.

If φ×R/f² exceeds the upper limit of the conditional expression (9), theeye relief R becomes too long, which increases the size of the opticalsystem. If φ×R/f² is lower than the lower limit of the conditionalexpression (9), on the other hand, the eye relief R becomes too short,which makes observation difficult. The pupil diameter φ also decreases,so an eclipse tends to occur, and observation of an image becomesdifficult when the optical system is used. The shape of the pupil neednot be circular, but may be rectangular or elliptic according to theapplication or design specification. This shape of the pupil can beimplemented by considering the shape of the lens and shape of the stop.In the conditional expression (9), it is preferable that the upper limitof φ×R/f² is 1.0 and the lower limit thereof is 0.15. Also in theconditional expression (9), it is more preferable that the upper limitof φ×R/f² is 1.0 and the lower limit thereof is 0.2. It is even morepreferable that φ×R/f² is around 0.3.

When the optical system of the present embodiment is actuallyconstructed, it is more preferable to satisfy the following conditions.

First to maintain good moldability and to insure excellent massproducibility for the first and second optical elements, it ispreferable that a viscosity (viscosity of uncured material) of amaterial constituting one of the optical element is at least 40 Pa·s(pascal-second) or more. If this viscosity is 40 Pa·s or less, resintends to flow during molding, making precise shape formation difficult.However the viscosity of a material constituting the other opticalelement is 2000 Pa·s or more.

In order to improve the production efficiency, it is preferable that thefirst and second optical elements are both formed using UV curableresin. Thereby the man hours can be decreased and cost can be decreased.

If the materials of the first and second optical elements are bothresin, as mentioned above, it is preferable that the specific gravitiesof these resins are both 2.0 or less to decrease size and weight. Resin,which has a lower specific gravity than glass, is very useful fordecreasing the weight of the optical system. To be even more effective,the specific gravity is more preferably 1.6 or less. The first andsecond optical elements have a refractive surface that have positiverefractive power on the interface with air, and this refractive surfaceis preferably aspherical.

It is also possible to mix dye in one of the resins of the first andsecond optical elements, so as to provide a color filter effect. Forexample, an infrared cut filter may be constructed by this method,whereby a compact image sensing optical system may be implemented.

The stop can be disposed at an arbitrary location in the optical system,but it is preferable to construct a stop so as to cut unnecessary raysand transmit only rays that are useful for image formation. For example,the lens frame itself may be used as an aperture stop, or the stop maybe constructed using a mechanical element at a position distant from thelens. The shape of the stop is not limited to a circle, but may berectangular or elliptic, according to the design specification.

If the optical system of the present embodiment is used for aphotographic optical system, an optical low pass filter may be includedinside or outside the contact multi-layer diffractive optics.

If the optical system of the present embodiment is used for anobservation optical system, it is preferable that the magnification ofthe magnifying glass thereof is ×2 or more, ×20 or less.

An optical system comprised of three or more (plurality of) composingelements where the contact multi-layer diffractive optics is enclosed isnot outside the scope of the present invention. An optical system inwhich a refractive index distributed lens, a crystal material lens orthe like, is also within the scope of the present invention.

It is also preferable to satisfy the condition given by the followingconditional expression (10),

0.001<Δ/f<0.02   (10)

where Δ is the maximum spread width of a d-line, g-line, C-line orF-line in the axial chromatic aberration.

The conditional expression (10) specifies the condition of anappropriate correction range of the axial chromatic aberration. If Δ/fexceeds the upper limit of the conditional expression (10), the axialchromatic aberration increases too much, which colors the image anddiminishes the image quality considerably. In the conditional expression(10), it is more preferable that the upper limit of Δ/f is 0.003, andthe lower limit thereof is 0.002.

Examples

Each example of the present invention will now be described withreference to the accompanying drawings. In each example, the phasedifference of the diffractive optical surface is calculated by an ultrahigh refractive index method using a regular refractive index and thelater mentioned aspherical expressions (23) and (24). The ultra highrefractive index method uses a predetermined equivalent relationshipbetween the aspherical shape and grating pitch on the diffractiveoptical surface, and in the present examples, the diffractive opticalsurface is shown by the data of the ultra high refractive index method,that is, by the later mentioned aspherical expressions (23) and (24),and the coefficients thereof. In the present example, the calculationtargets of the aberration characteristic are d-line (wavelength: 587.6nm, refractive index: 10001), C-line (wavelength: 656.3 nm, refractiveindex: 11170.4255), F-line (wavelength: 486.1 nm, refractive index:8274.7311) and g-line (wavelength: 435.8 nm, refractive index7418.6853).

In each example, the aspherical surface is given by the followingconditional expressions (23) and (24),

S(y)=(y ² /r)/(1+(1−κ·y ² /r ²)^(1/2) }+C ₂ y ² +C ₄ y ⁴ +C ⁶ y ⁶ +C ₈ y⁸ +C ₁₀ y ¹⁰   (23)

R=1/{(1/r)+2C ₂}  (24)

where y is the height in a direction vertical to the optical axis, S(y)is a distance (sag amount) from the tangential plane at a vertex of theaspherical surface to a position on the aspherical surface at the heighty along the optical axis, r is a radius of curvature of the referencespherical surface, R is a paraxial radius of curvature, κ is a conicalcoefficient, and C_(n) is an aspherical coefficient of degree n.

In each example, * is indicated at the right side of the surface numberin the table if the lens surface is aspherical. In each example, thephase difference of the diffractive optical surface is calculated by theultra refractive index method using the regular refractive index and theabove mentioned aspherical expressions (23) and (24). Therefore theaspherical expressions (23) and (24) are used for both the asphericallens surface and the diffractive optical surface, but the asphericalexpressions (23) and (24) used for the aspherical lens surface show theaspherical shape of the lens surface itself, while the asphericalexpressions (23) and (24) used for the diffractive optical surface showthe performance of the diffractive optical surface.

Example 1

Now Example 1 of the present invention will be described with referenceto FIG. 2 to FIG. 4. The optical system of each example is used as aneye piece to observe an image of an object. As FIG. 2 shows, an opticalsystem (eye piece) EL1 of Example 1 is comprised of a first lens L1having a positive refractive power and a second lens L2 having apositive refractive power, which are disposed in order from an object O,and a contact multi-layer diffractive optics DOE is glued on a surfaceof the first lens L1 facing the object O. In FIG. 2, an exit pupil isindicated by the symbol H. The object O is a liquid crystal displaydevice, for example, and an image displayed on the liquid crystaldisplay device is enlarged and observed using the optical system (eyepiece) EL1 of the present example. The full angle of view of thisoptical system (eye piece) EL1 is 35.4 degrees.

The contact multi-layer diffractive optics DOE is comprised of a firstoptical element 51 and a second optical element 52 in order from theside glued to the first lens L1. The surface of the first lens L1 facingthe object O is a concave surface having a slight curvature, and thesurface of the first lens L1 positioned opposite the object O side(surface facing the second lens L2) is a convex surface. The surface ofthe second lens L2 facing the first lens L1 is a convex surface, and thesurface of the second lens L2 positioned opposite the first lens L1 sideis a concave surface.

In the present example, materials of the first and second lenses L1 andL2 are both Zeonex 480R, made by Zeon Corp., where the material of thefirst optical element 51 is an ultraviolet curable resin having arelatively low refractive index and high dispersion, and the material ofthe second optical element 52 is an ultraviolet curable resin having arelatively high refractive index and low dispersion, which will bedescribed below.

The above mentioned ultraviolet curable resin having a relatively lowrefractive index and high dispersion is an ultraviolet curable compositegenerated by mixing 2,2,3,3,4,4,5,5-octaflu-ohexane-1,6-di-acrylate,9,9-bis[4-(2-acryloyloxyethoxy)phenyl]fluorene, and Irgacure 184, andperforming a predetermined operation. Hereafter this resin is called lowrefractive index resin No. 1. The ultraviolet curable resin having arelatively high refractive index and low dispersion is an ultravioletcurable composite generated by performing an additional reaction oftricyclodecane-dimethanol diacrylate and di(2-mercapto diethyl)sulfide,then adding Irgacure 184. Hereafter this resin is called high refractiveindex resin No. 1.

Table 1 below shows the parameters of each lens according to Example 1.In Table 1, the surface numbers 1 to 8 correspond to the surfaces 1 to 8in FIG. 2. The first surface is a pupil surface r in Table 1 is a radiusof curvature of the lens surface (radius of curvature of a referencespherical surface in the case of an aspherical surface), d is a distanceof lens surfaces, n(d) is a refractive index on d-line, n(g) is arefractive index on g-line, n(C) is a refractive index on C-line, andn(F) is a refractive index on F-line. The values corresponding to theabove mentioned conditional expressions (1) to (10) (excluding theconditional expression (3)), that is the conditional correspondencevalues, are also shown below. In the following parameter values, “mm” isnormally used as a unit for the radius of curvature r, surface distanced and other lengths, unless otherwise specified, however a similaroptical performance can be acquired even if the optical system isproportionally expanded or reduced, so unit is not limited to “mm”, butanother appropriate unit can also be used. The above description on thetables is the same for other examples.

In Table 1, * is indicated at the right side of the surface number ifthe lens surface is aspherical. In the present example, surfacescorresponding to the surface numbers 3 and 7 are aspherical, and asurface corresponding to the surface number 6 is a diffractive opticalsurface. The diffractive optical surface is represented by a combinationof an ultra high refractive index value, such as n(d)=10001, and anaspherical surface coefficient.

TABLE 1 Surface number r d n(d) n(g) n(C) n(F) 1 0.00000 21.000001.000000 2 −300.00000 4.00000 1.524700 1.536490 1.521960 1.531290 3*−26.22573 0.20000 1.000000 4 28.31486 4.00000 1.524700 1.536490 1.5219601.531290 5 297.99863 0.20000 1.527600 1.547700 1.523300 1.538500 6*297.99863 0.00000 10001 7418.6853 11170.4255 8274.7311 7* 297.998630.20000 1.556900 1.571100 1.553700 1.564800 8 297.99863 23.078111.000000 (Aspherical data) Surface number κ C₂ C₄ C₆ C₈ C₁₀ 3 0.4700 0.00000 −8.00000 × 10⁻⁶     1.38460 × 10⁻⁹ 2.00000 × 10⁻¹² 0.00000 71.0000 −1.90000 × 10⁻⁷ 3.00000 × 10⁻¹⁰ 0.00000 0.00000 0.00000(Conditional correspondence values) D = 0.2 f = 25.812 f1 = 48.847 f2 =54.496 Δνd = 15.46 Δnd = 0.0293 Eg = 98.221 EC = 98.233 Ed = 99.999 C =24.19 h = 0.02 d = 0.2 p = 0.0238 φ = 10.000 r = 21.000 Δ = 0.1873(1)D/f = 0.00775 (2)D/(f1 × f2) = 0.0000751 (4)Δνd/Δnd = 527.645(5)(Eg + EC)/2 = 98.227 0.9 × Ed = 89.999 (6)C/f = 0.937 (7)h/d = 0.1(8)p/f = 0.000922 (9)φ × R/f² = 0.3152 (10)Δ/f = 0.00726

As the above table shows, the present example satisfies all theconditional expressions (1) to (10) (excluding the conditionalexpression (3)).

FIG. 3 are graphs showing various aberrations according to Example 1.Each graph shows the result of aberrations on d-line, g-line, C-line andF-line, where FNO is an F number, and Y is an image height. In the graphof the spherical aberration, a value of the F number corresponding tothe maximum aperture is shown, in the graphs of the astigmatism anddistortion, the maximum values of the image height are shownrespectively, and in the graph of the coma aberration, the value of eachimage height is shown. In the graph showing astigmatism, the solid lineindicates a sagittal image surface, and the broken line indicates ameridional image surface. The above description of the graphs showingaberrations is the same for other examples. As each of the graphsshowing aberrations clarifies, according to the present example, variousaberrations are well corrected, and excellent image formationperformance is implemented not only for d-line, but also for g-line,C-line and F-line.

The curves A and B in FIG. 4 show the distribution of the diffractionefficiency when it is set that the diffraction efficiency on d-line is100%, where the curve A shows the diffraction efficiency in a singlelayer diffractive optics in which a relief pattern is formed on thesurface of the low refractive index resin No. 1, and the curve B showsthe diffraction efficiency in the contact multi-layer diffractive opticsformed by the low refractive index resin No. 1 and the high refractiveindex resin No. 1. In the present example, 0.95 (95%) or higherdiffraction efficiency (light intensity) can be implemented in awavelength area from g-line to C-line.

Example 2

Example 2 will now be described with reference to FIG. 5 and FIG. 6. AsFIG. 5 shows, an optical system (eye piece) EL2 of Example 2 iscomprised of a first lens L1 having a negative refractive power and asecond lens L2 having a positive refractive power, which are disposed inorder from an object O, and a contact multi-layer diffractive optics DOEis glued on a surface of the first lens L1 facing the object O. In FIG.5, an exit pupil is indicated by the symbol H. The full angle of view ofthis optical system (eye piece) EL2 is 24.3 degrees.

As FIG. 5 shows, the optical system (eye piece) EL2 of Example 2 has asimilar configuration as the optical system EL1 of Example 1, so eachcomposing element is denoted with a same symbol as Example 1, for whichdetailed description is omitted. A difference from Example 1 is that thefirst lens L1 has a negative refractive power. Another difference fromExample 1 is that the surface of the second lens L2 positioned at theopposite side of the first lens L1 has a concave surface.

Table 2 shows the parameters of each lens according to Example 2. InTable 2, the surface numbers 1 to 8 correspond to the surfaces 1 to 8 inFIG. 5. In Table 2, * is indicated at the right side of the surfacenumber if the lens surface is aspherical. In the present example,surfaces corresponding to the surface numbers 3, 4 and 7 are aspherical,and a surface corresponding to the surface number 6 is a diffractiveoptical surface. The diffractive optical surface is represented by theultra high refractive index method, just like Example 1.

TABLE 2 Surface number r d n(d) n(g) n(C) n(F) 1 0.00000 21.000001.000000 2 34.04256 4.60000 1.524700 1.536490 1.521960 1.531290 3*−19.63227 0.10000 1.000000 4* 140.45480 2.50000 1.517420 1.5298001.514440 1.524310 5 49.47642 0.20000 1.527600 1.547700 1.523300 1.5385006* 49.47642 0.00000 10001 7418.6853 11170.4255 8274.7311 7* 49.476420.20000 1.556900 1.571100 1.553700 1.564800 8 49.47642 22.76128 1.000000(Aspherical data) Surface number κ C₂ C₄ C₆ C₈ C₁₀ 3 −1.7871  0.000001.78450 × 10⁻⁴ −1.65830 × 10⁻⁶ 7.11790 × 10⁻⁹ −6.18770 × 10⁻¹² 4 −6.5471 0.00000 1.86590 × 10⁻⁴ −1.49880 × 10⁻⁶ 6.23320 × 10⁻⁹ −2.70900 × 10⁻¹²7 1.0000 −1.50000 × 10⁻⁷  7.68750 × 10⁻¹¹  −1.03410 × 10⁻¹¹  1.78730 ×10⁻¹³ −9.74580 × 10⁻¹⁶ (Conditional correspondence values) D = 0.1 f =26.335 f1 = −269.234 f2 = 24.452 Δνd = 15.46 Δnd = 0.0293 Eg = 98.221 EC= 98.233 Ed = 99.999 C = 18.71 h = 0.02 d = 0.2 p = 0.0305 φ = 10.000 r= 21.000 Δ = 0.1124 (1)D/f = 0.00380 (3)D/(f1 × f2) = −0.00001519(4)Δνd/Δnd = 527.645 (5)(Eg + EC)/2 = 98.227 0.9 × Ed = 89.999 (6)C/f =0.711 (7)h/d = 0.1 (8)p/f = 0.00116 (9)φ × R/f² = 0.3028 (10)Δ/f =0.00427

As the above table shows, the present example satisfies all theconditional expressions (1) to (10) (excluding the conditionalexpression (2)).

FIG. 6 are graphs showing various aberrations according to Example 2. Aseach of the graphs showing aberrations clarifies, according to thepresent example, various aberrations are well corrected, and excellentimage formation performance is implemented not only for d-line, but alsofor g-line, C-line and F-line.

Example 3

Example 3 will now be described with reference to FIG. 7 and FIG. 8. AsFIG. 7 shows, an optical system (eye piece) EL3 of Example 3 iscomprised of a first lens L11 having a positive refractive power, and asecond lens L12 having a positive refractive power, which are disposedin order from an object O, and a contact multi-layer diffractive opticsDOE is glued on a surface of the second lens L12 facing the first lensL11. In FIG. 7, the exit pupil is indicated by the symbol H. The fullangle of view of this optical system (eye piece) EL3 is 40.0 degrees.

The contact multi-layer diffractive optics DOE is comprised of a firstoptical element 51 and a second optical element 52 in order from theside glued to the second lens L12. The surface of the first lens L11facing the object O is a plane, and the surface of the first lens L11positioned opposite of the object O side (surface facing the second lensL12) is a convex surface. The surface of the second lens L12 facing thefirst lens L11 is a convex surface, and the surface of the second lensL12 positioned opposite of the first lens L11 side is a plane.

In the present example, materials of the first and second lenses L11 andL12 are both acrylic resin, where the material of the first opticalelement 51 is an ultraviolet curable resin having a relatively highrefractive index and low dispersion (just like the above mentionedExample 1), and the material of the second optical element 52 is anultraviolet curable resin having a relatively low refractive index andhigh dispersion (just like the above mentioned Example 1).

Table 3 shows the parameters of each lens according to Example 3. InTable 3, the surface numbers 1 to 8 correspond to the surfaces 11 to 18in FIG. 7. In Table 3, * is indicated at the right side of the surfacenumber if the lens surface is aspherical. In the present example, asurface corresponding to the surface number 5 is aspherical, and asurface corresponding to the surface number 4 is a diffractive opticalsurface. The diffractive optical surface is represented by the ultrahigh refractive index method, just like Example 1.

TABLE 3 Surface number r d n(d) n(g) n(C) n(F) 1 0.00000 5.000001.000000 2 0.00000 2.00000 1.491080 1.501900 1.488540 1.497070 3−8.20000 0.20000 1.556900 1.571100 1.553700 1.564800 4* −8.20000 0.0000010001 7418.6853 11170.4255 8274.7311 5* −8.20000 0.20000 1.5276001.547700 1.523300 1.538500 6 −8.20000 13.00000 1.000000 7 8.200003.00000 1.491080 1.501900 1.488540 1.497070 8 0.00000 0.20254 1.000000(Aspherical data) Surface number κ C₂ C₄ C₆ C₈ C₁₀ 5 1.0000 −2.20000 ×10⁻⁷ −2.00000 × 10⁻⁹ 0.00000 0.00000 0.00000 (Conditional correspondencevalues) D = 13 f = 13.47645 f1 = 15.537 f2 = 16.698 Δνd = 15.46 Δnd =0.0293 Eg = 98.221 EC = 98.233 Ed = 99.999 C = 6.38 h = 0.02 d = 0.2 p =0.01203 φ = 10.000 r = 21.000 Δ = 0.0488 (1)D/f = 0.9646 (2)D/(f1 × f2)= 0.0501 (4)Δνd/Δnd = 527.645 (5)(Eg + EC)/2 = 98.227 0.9 × Ed = 89.999(6)C/f = 0.4734 (7)h/d = 0.1 (8)p/f = 0.000893 (9)φ × R/f² = 1.1563(10)Δ/f = 0.00362

As the above table shows, the present example satisfies all theconditional expression (1) to (10) (excluding the conditional expression(3)).

FIG. 8 are graphs showing various aberrations according to Example 3. Aseach of the graphs showing aberrations clarifies, according to thepresent example, various aberrations are well corrected although not aswell corrected as those in the abovementioned first and second examples,and excellent image formation performance is implemented not only ford-line, but also for g-line, C-line and F-line. In each example, thepresent inventor attempted to design the optical system under thecondition of D/f≈0.003, but a major improvement of various aberrationswas not implemented compared with prior art.

The present invention described above is not limited to the aboveembodiments, but can be improved appropriately within a scope that doesnot deviate from the spirit of the present invention. Each of the abovementioned examples described an example of the optical system used as aneye piece, but the optical system of the present invention is notlimited to this, but may be used for a projection optical system aswell. In the case of an eye piece, it is preferable to form a contactmulti-layer diffractive optics on the lens at the object side, as seenin Examples 1 and 2. This is because flares decreases since theprincipal ray enters roughly vertically to the optical surface on whichthe relief pattern is formed.

1. An optical system comprising a first lens and a second lens having apositive refractive power, which are disposed in order from an object,characterized in that a contact multi-layer diffractive optics, whichhas a first optical element formed with a relief pattern and a secondoptical element, which is in contact with the surface of the firstoptical element where the relief pattern is formed, is disposed on anoptical surface of the first lens or the second lens.
 2. The opticalsystem according to claim 1, characterized in that the difference ofrefractive indexes on a d-line between the first optical element and thesecond optical element is 0.45 or less, and the following expression issatisfied:0.002<D/f<2.0 where D is an air distance on an optical axis between thefirst lens and the second lens, and f is a focal length of the entireoptical system.
 3. The optical system according to claim 2,characterized in that the condition of the following expression issatisfied:0<D/(f1×f2)<0.15 where f1 is a focal length of the first lens, f2 is afocal length of the second lens, and f1>0 and f2>0.
 4. The opticalsystem according to claim 2, characterized in that the condition of thefollowing expression is satisfied:−0.1<D/(f1×f2)<0 where f1 is a focal length of the first lens, f2 is afocal length of the second lens, and f1<0, f2>0 and |f1|>|f2|.
 5. Theoptical system according to claim 1, characterized in that at least oneoptical surface of the first lens and the second lens is aspherical. 6.The optical system according to claim 1, characterized in that thecontact multi-layer diffractive optics is formed on a surface of thefirst lens, the face facing the object.
 7. The optical system accordingto claim 1, characterized in that the first optical element is formedusing one of a material having a relatively high refractive index andlow dispersion, and a material having a relatively low refractive indexand high dispersion, and the second optical element is formed using theother one of the materials, and the condition of the followingexpression is satisfied:50<Δνd/Δnd<2000 where Δνd is a difference of Abbe numbers between thefirst optical element and the second optical element, and Δnd is adifference of refractive indexes on a d-line between the first opticalelement and the second optical element.
 8. The optical system accordingto claim 1, characterized in that the condition of the followingexpression is satisfied:(Eg+EC)/2>0.9×Ed where Ed is a diffraction efficiency of the contactmulti-layer diffractive optics on a d-line, Eg is a diffractionefficiency of the contact multi-layer diffractive optics on a g-line,and EC is a diffraction efficiency of the contact multi-layerdiffractive optics on a C-line.
 9. The optical system according to claim1, characterized in that the condition of the following expression issatisfied:0.0001<p/f<0.003 where p is a minimum pitch of the relief pattern and fis a focal length of the entire optical system.
 10. The optical systemaccording to claim 1, characterized in that the condition of thefollowing expression is satisfied:0.1<φ×R/f ²<2.0 where f is a focal length of the entire optical system,φ is a pupil diameter, and R is eye relief.
 11. An eye piece forobserving an image of an object, the eyepiece comprising an opticalsystem, and the optical system comprising a first lens and a second lenshaving a positive refractive power, which are disposed in order from anobject, the optical system being characterized in that a contactmulti-layer diffractive optics, which has a first optical element formedwith a relief pattern and a second optical element, which is in contactwith the surface of the first optical element where the relief patternis formed, is disposed on an optical surface of the first lens or thesecond lens.